Hello.
I would like to suggest the option that a new conversation, which is not assigned to any department, can be immediately assigned to one. Since the administrator only cares about viewing and not responding, which results in conversations not assigned by departments and not resolved.
On the other hand, the admin when entering a chat, immediately marks the message as read, an option that allows not reading the chats, but viewing the messages would be ideal, and thus the administrator can keep track of his employees but not interfere and mark messages as read.

I also suggest the option of signature on each message, so that each message contains at the beginning the name of the department or the agent, example

"*Sales Department*:
Hello thanks for writing to us"

And thus each message would have its label until it leaves the chat.

Thank you very much

Thanks for your suggestion. We will consider your request in future.

Thanks

Hi! Great, please check out my other threads.
When do you plan to update?
About the suggestion I said here that admin does not read messages, it could be that if your account is out of support service then don't mark any message as read, this could be for any account not just admin

Thanks